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Existence of the Limit Value of Two Person Zero-Sum Discounted Repeated Games via Comparison Theorems

Author

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  • Sylvain Sorin

    (Université P. et M. Curie Paris 6
    Ecole Polytechnique)

  • Guillaume Vigeral

    (Université Paris-Dauphine)

Abstract

We give new proofs of existence of the limit of the discounted values for two person zero-sum games in the three following frameworks: absorbing, recursive, incomplete information. The idea of these new proofs is to use some comparison criteria.

Suggested Citation

  • Sylvain Sorin & Guillaume Vigeral, 2013. "Existence of the Limit Value of Two Person Zero-Sum Discounted Repeated Games via Comparison Theorems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 564-576, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0193-4
    DOI: 10.1007/s10957-012-0193-4
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    3. MERTENS, Jean-François & ZAMIR, Shmuel, 1971. "The value of two-person zero-sum repeated games with lack of information on both sides," LIDAM Reprints CORE 154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Laraki, Rida & Renault, Jérôme, 2017. "Acyclic Gambling Games," TSE Working Papers 17-768, Toulouse School of Economics (TSE).
    2. Rida Laraki & Jérôme Renault, 2020. "Acyclic Gambling Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1237-1257, November.
    3. Sylvain Sorin & Guillaume Vigeral, 2020. "Limit Optimal Trajectories in Zero-Sum Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 555-572, June.
    4. repec:dau:papers:123456789/10880 is not listed on IDEAS
    5. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    6. Guillaume Vigeral, 2013. "A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value," Dynamic Games and Applications, Springer, vol. 3(2), pages 172-186, June.

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